the 59 stellations of the icosahedron

[jacpot]

Hello everyone,
I am starting to manufacture the 59 stellations of the icosahedron.
I notice inconsistencies in the numbering of the stellations,
depending on the sites it is different:
_ by Stella software
_ here; http://www.mathconsult.ch/static/icosah ... graph.html
_ here; https://en.wikipedia.org/wiki/The_Fifty-Nine_Icosahedra
_ here; https://web.archive.org/web/20110516141 ... i/i011.htm

What is the correct numbering?
Sincerely


bonjour à tous,
je commence la fabrication des 59 stellations de l' icosaèdre.
je constate des incohérences dans la numérotation des stellations,
selon les sites elle est différente:
_ par le logiciel Stella
_ ici; http://www.mathconsult.ch/static/icosah ... graph.html
_ ici; https://en.wikipedia.org/wiki/The_Fifty-Nine_Icosahedra
_ ici; https://web.archive.org/web/20110516141 ... i/i011.htm

Qu' elle est la bonne numérotation?
cordialement

[robertw]

I don't know that there is a "correct" numbering system. The numbering was somewhat arbitrary in The 59 Icosahedra I think. Stella is able to find stellations of any polyhedron, so it has to proceed in a logical fashion, so it won't match The 59 Icosahedra. There would be more than one way to enumerate the stellations in a logical way though, so Stella's way isn't "correct" either. There is no obvious correct way.

[jacpot]

thank you Robert,
I don't know yet how I'm going to proceed,
Thank you for your reply
cdlt

[guy]

There are many more stellations of the icosahedron, being the ones which do not come under "Miller's rules".
Some are also quite beautiful.
A selection, which various people have pointed out to me over the years, may be found here: https://www.steelpillow.com/polyhedra/icosa/lost/lost.html